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Robert Rosenbaum

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Neurons and Cognition Quantitative Methods

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preprint2026arXiv

Empirical scaling laws in balanced networks with conductance-based synapses

Strongly coupled, recurrent, balanced network models have been successful in describing and predicting many phenomena observed in cortical neural recordings. However, most balanced network models use current-based synapse models in place of more realistic, conductance-based models. Conductance-based synapse models predict unrealistically small membrane potential variability. On the other hand, introducing realistic levels of spike time correlations to models with current-based synapses predicts unrealistically large membrane potential variability. We use computer simulations to show that these two effects can cancel: Recurrent network models with conductance-based synapses and spike time correlations produce more realistic, moderate levels of membrane potential variability. Consistent with recent work on feedforward networks, our results show that including more realistic modeling assumptions produces more realistic dynamics, but only if when two modeling assumptions are included together.

preprint2022arXiv

Evaluating the extent to which homeostatic plasticity learns to compute prediction errors in unstructured neuronal networks

The brain is believed to operate in part by making predictions about sensory stimuli and encoding deviations from these predictions in the activity of "prediction error neurons." This principle defines the widely influential theory of predictive coding. The precise circuitry and plasticity mechanisms through which animals learn to compute and update their predictions are unknown. Homeostatic inhibitory synaptic plasticity is a promising mechanism for training neuronal networks to perform predictive coding. Homeostatic plasticity causes neurons to maintain a steady, baseline firing rate in response to inputs that closely match the inputs on which a network was trained, but firing rates can deviate away from this baseline in response to stimuli that are mismatched from training. We combine computer simulations and mathematical analysis systematically to test the extent to which randomly connected, unstructured networks compute prediction errors after training with homeostatic inhibitory synaptic plasticity. We find that homeostatic plasticity alone is sufficient for computing prediction errors for trivial time-constant stimuli, but not for more realistic time-varying stimuli. We use a mean-field theory of plastic networks to explain our findings and characterize the assumptions under which they apply.

preprint2020arXiv

Synaptic Plasticity in Correlated Balanced Networks

The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory--inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in plastic neural networks. In particular, it is not fully understood how plasticity induced changes in the network affect balance, and in turn, how correlated, balanced activity impacts learning. How does the dynamics of balanced networks change under different plasticity rules? How does correlated spiking activity in recurrent networks change the evolution of weights, their eventual magnitude, and structure across the network? To address these questions, we develop a general theory of plasticity in balanced networks. We show that balance can be attained and maintained under plasticity induced weight changes. We find that correlations in the input mildly, but significantly affect the evolution of synaptic weights. Under certain plasticity rules, we find an emergence of correlations between firing rates and synaptic weights. Under these rules, synaptic weights converge to a stable manifold in weight space with their final configuration dependent on the initial state of the network. Lastly, we show that our framework can also describe the dynamics of plastic balanced networks when subsets of neurons receive targeted optogenetic input.

preprint2016arXiv

Highly connected neurons spike less frequently in balanced networks

Many biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability. In balanced networks, strong excitatory synaptic inputs are canceled by strong inhibitory inputs on average and spiking activity is driven by transient breaks in this balance. Most previous studies of balanced networks assume a homogeneous or distance-dependent connectivity structure, but connectivity in biological cortical networks is more intricate. We use a heterogeneous mean-field theory of balanced networks to show that heterogeneous in-degrees can break balance, but balance can be restored by heterogeneous out-degrees that are correlated with in-degrees. In all examples considered, we find that highly connected neurons spike less frequently, consistent with recent experimental observations.

preprint2013arXiv

Balanced networks of spiking neurons with spatially dependent recurrent connections

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the spatial separation between neurons. In the continuum limit we derive that stable, balanced firing rate solutions require that the spatial spread of external inputs be broader than that of recurrent excitation, which in turn must be broader than or equal to that of recurrent inhibition. For finite size networks we investigate the pattern forming dynamics arising when balanced conditions are not satisfied. The spatiotemporal dynamics of balanced networks offer new challenges in the statistical mechanics of complex systems.

preprint2012arXiv

The impact of short term synaptic depression and stochastic vesicle dynamics on neural variability

Neural variability plays a central role in neural coding and neuronal network dynamics. Unreliability of synaptic transmission is a major source of neural variability: synaptic neurotransmitter vesicles are released probabilistically in response to presynaptic spikes and are recovered stochastically in time. The stochastic dynamics of this process interacts with variability in the arrival times of presynaptic spikes to shape the variability of the postsynaptic response. We use continuous time Markov chain methods to analyze a model of short term synaptic depression with stochastic vesicle dynamics coupled with three different models of presynaptic spiking: one model in which the timing of presynaptic spikes are modeled as a Poisson process, one in which spikes occur more regularly than a Poisson process and one in which spikes occur more irregularly. We use this analysis to investigate how variability in a presynaptic spike train is transformed by short term synaptic depression and stochastic vesicle dynamics to determine the variability of the postsynaptic response to a presynaptic spike train. We find that regular presynaptic spiking increases the average rate at which vesicles are released, that the number of vesicles released over a time window is more variable for smaller time windows than for larger time windows, and that fast presynaptic spiking gives rise to Poisson-like variability of the postsynaptic response even when presynaptic spike times are highly non-Poisson. Our results complement and extend previously reported theoretical results and provide possible explanations for some trends observed in recorded data.

preprint2010arXiv

Finite volume and asymptotic methods for stochastic neuron models with correlated inputs

We consider a pair of stochastic integrate and fire neurons receiving correlated stochastic inputs. The evolution of this system can be described by the corresponding Fokker-Planck equation with non-trivial boundary conditions resulting from the refractory period and firing threshold. We propose a finite volume method that is orders of magnitude faster than the Monte Carlo methods traditionally used to model such systems. The resulting numerical approximations are proved to be accurate, nonnegative and integrate to 1. We also approximate the transient evolution of the system using an Ornstein--Uhlenbeck process, and use the result to examine the properties of the joint output of cell pairs. The results suggests that the joint output of a cell pair is most sensitive to changes in input variance, and less sensitive to changes in input mean and correlation.